Problem: Which of the following numbers is a factor of 180? ${7,8,11,12,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $180$ by each of our answer choices. $180 \div 7 = 25\text{ R }5$ $180 \div 8 = 22\text{ R }4$ $180 \div 11 = 16\text{ R }4$ $180 \div 12 = 15$ $180 \div 13 = 13\text{ R }11$ The only answer choice that divides into $180$ with no remainder is $12$ $ 15$ $12$ $180$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $180$ $180 = 2\times2\times3\times3\times5 12 = 2\times2\times3$ Therefore the only factor of $180$ out of our choices is $12$. We can say that $180$ is divisible by $12$.